Antenna coupling component measurement tool having rotating antenna configuration

ABSTRACT

Disclosed herein are electromagnetic resistivity logging systems and methods that employ an antenna configuration having at most two transmitter or receiver antenna orientations that rotate relative to the borehole. The measurements made by this reduced-complexity antenna configuration enable the determination of at least seven components of a coupling matrix, which may be determined using a linear system of equations that express the azimuthal dependence of the measurements. For increased reliability, measurement averaging may be performed in azimuthally spaced bins. The coupling matrix components can then be used as the basis for determining logs of various formation parameters, including vertical resistivity and anisotropy.

BACKGROUND

The basic principles and techniques for electromagnetic logging forearth formations are well known. For example, induction logging todetermine the resistivity (or its inverse, conductivity) of earthformations adjacent a borehole has long been a standard and importanttechnique in the search for and recovery of subterranean petroleumdeposits. In brief, a transmitter transmits an electromagnetic signalthat passes through formation materials around the borehole and inducesa signal in ore or more receivers. The amplitude and/or phase of thereceiver signals are influenced by the formation resistivity, enablingresistivity measurements to be made. The measured signal characteristicsand/or formation properties calculated therefrom are recorded as afunction of the tool's depth or position in the borehole, yielding aformation log that can be used by analysts.

Note, however, that the resistivity of a given formation may beisotropic (equal in all directions) or anisotropic (unequal in differentdirections). In electrically anisotropic formations, the anisotropy isgenerally attributable to extremely fine layering during the sedimentarybuild-up of the formation. Hence, in a formation coordinate systemoriented such that the x-y plane is parallel to the formation layers andthe z axis is perpendicular to the formation layers, resistivities R_(X)and R_(Y) in directions x and y, respectively, tend to be the same, butresistivity R_(Z) in the z direction is different. Thus, the resistivityin a direction parallel to the plane of the formation (i.e., the x-yplane) is known as the horizontal resistivity, R_(H), and theresistivity in the direction perpendicular to the plane of the formation(i.e., the z direction) is known as the vertical resistivity, R_(V). Theindex of anisotropy, η, is defined as η=[R_(V)/R_(H)]^(1/2).

As a further complication to measuring formation resistivity, boreholesare generally not perpendicular to formation beds. The angle between theaxis of the well bore and the orientation of the formation beds (asrepresented by the normal vector) has two components. These componentsare the dip angle and the strike angle. The dip angle is the anglebetween the borehole axis and the normal vector for the formation bed.The strike angle is the direction in which the boreholes axis “leansaway from” the normal vector. (These will be defined more rigorously inthe detailed description.)

Electromagnetic resistivity logging measurements are a complex functionof formation resistivity, formation anisotropy, and the formation dipand strike angles, which may all be unknown. Logging tools that fail toaccount for one or more of these parameters may provide measurementquality that is less than ideal. Conversely, tools that can be used tomeasure each of these parameters will provide improved resistivitymeasurements. Moreover, tools that are able to provide dip and strikemeasurements along with azimuthal orientation information, can be usedfor geosteering. (Geosteering is a process in which drill engineersadjust the drilling direction to increase the borehole's exposure to ahydrocarbon-bearing formation (the “payzone”).)

BRIEF DESCRIPTION OF THE DRAWINGS

A better understanding of the various disclosed embodiments can beobtained when the following detailed description is considered inconjunction with the following drawings, in which:

FIG. 1 shows an illustrative logging while drilling environmentincluding dipping formation beds;

FIG. 2 shows an illustrative wireline logging environment includingdipping formation beds;

FIG. 3 shows a relationship between the orientation of a borehole and adipping formation bed;

FIG. 4 shows a hypothetical antenna arrangement for a tool having anorthogonal triaxial transmitter and two orthogonal triaxial receivers;

FIG. 5 shows angles for defining the orientation of a tilted antenna;

FIG. 6 is a block diagram of an illustrative electronics module for anelectromagnetic resistivity tool;

FIG. 7 shows an illustrative electromagnetic resistivity logging toolhaving tilted transmitter and receiver antennas;

FIG. 8 is a flow diagram of an illustrative electromagnetic resistivitylogging method;

FIG. 9 shows an illustrative electromagnetic resistivity logging toolhaving parallel tilted transmitter and receiver antennas;

FIG. 10 shows an illustrative electromagnetic resistivity logging toolhaving transmitters tilted at a first orientation and receiver antennastilted at a second orientation;

FIG. 11 shows an illustrative electromagnetic resistivity logging toolhaving both parallel and non-parallel tilted transmitter and receiverantennas;

FIG. 12 shows an illustrative electromagnetic resistivity logging toolhaving co-located tilted receiver antennas;

FIG. 13 shows the division of a borehore circumference into azimuthalbins; and

FIG. 14 shows an illustrative electromagnetic resistivity logging toolhaving compensated measurements.

While the invention is susceptible to various modifications andalternative forms, specific embodiments thereof are shown by way ofexample in the drawings and will herein be described in detail. Itshould be understood, however, that the drawings and detaileddescription thereto are not intended to limit the invention to theparticular form disclosed, but on the contrary, the intention is tocover all modifications, equivalents and alternatives falling within thespirit and scope of the appended claims.

DETAILED DESCRIPTION

Disclosed herein are electromagnetic resistivity logging systems andmethods that employ rotation of an azimuthally sensitive antennaconfiguration to obtain more elements of a coupling matrix than could beobtained from the static antenna configuration alone. Such exploitationof the rotation enables a complete antenna coupling matrix to beobtained with a tool having only two antenna orientations. With thecomplete antenna coupling matrix, the various resistivity measurementparameters can be measured, including formation resistivity, formationanisotropy, and formation dip and strike angles. Moreover, when thecoupling matrix values are combined with orientation information fromthe tool, geosteering or boundary detection signals may be derived. Suchbenefits may be obtained with a reduced cost and greater reliability dueto the reduced number of antennas.

The disclosed tool configurations and operations are best understood inthe context of the larger systems in which they operate. Accordingly, anillustrative logging while drilling (LWD) environment is shown inFIG. 1. A drilling platform 2 supports a derrick 4 having a travelingblock 6 for raising and lowering a drill string 8. A kelly 10 supportsthe drill string 8 as it is lowered through a rotary table 12. A drillbit 14 is driven by a downhole motor and/or rotation of the drill string8. As bit 14 rotates, it creates a borehole 16 that passes throughvarious formations 18. A pump 20 circulates drilling fluid through afeed pipe 22 to kelly 10, downhole through the interior of drill string8, through orifices in drill bit 14, back to the surface via the annulusaround drill string 8, and into a retention pit 24. The drilling fluidtransports cuttings from the borehole into the pit 24 and aids inmaintaining the borehole integrity.

An electromagnetic resistivity logging tool 26 is integrated into thebottom-hole assembly near the bit 14. As the bit extends the boreholethrough the formations, logging tool 26 collects measurements relatingto various formation properties as well as the tool orientation andposition and various other drilling conditions. (The orientationmeasurements may be performed using an azimuthal orientation indicator,which may include magnetometers, inclinometers, and/or accelerometers,though other sensor types such as gyroscopes may be used. In someembodiments, the tool includes a 3-axis fluxgate magnetometer and a3-axis accelerometer.) The logging tool 26 may take the form of a drillcollar, i.e., a thick-walled tubular that provides weight and rigidityto aid the drilling process. A telemetry sub 28 may be included totransfer tool measurements to a surface receiver 30 and to receivecommands from the surface receiver.

More preferably, rotational position indicator 70 may contain both a3-axis fluxgate magnetometer and a 3-axis accelerometer. As is known inthe art, the combination of those two sensor systems enables themeasurement of the toolface, inclination, and azimuth orientation anglesof the borehole. The toolface and hole inclination angles are calculatedfrom the accelerometer sensor output. The magnetometer sensor outputsare used to calculate the hole azimuth. With the toolface, the holeinclination, and the hole azimuth information, a tool in accordance withthe present invention can be used to steer the bit to the desirable bed.Specifically, the response difference or the response ratio can be usedeffectively to enter a desired payzone or to stay within the payzone ofinterest.

At various times during the drilling process, the drill string 8 may beremoved from the borehole as shown in FIG. 2. Once the drill string hasbeen removed, logging operations can be conducted using a wirelinelogging tool 34, i.e., a sensing instrument sonde suspended by a cable42 having conductors for transporting power to the tool and telemetryfrom the tool to the surface. A resistivity imaging portion of thelogging tool 34 may have centralizing arms 36 that center the toolwithin the borehole as the tool is pulled uphole. A logging facility 44collects measurements from the logging tool 34, and includes computingfacilities for processing and storing the measurements gathered by thelogging tool.

FIG. 1 shows that the formations 18 are not perpendicular to theborehole, which may occur naturally or due to directional drillingoperations. The borehole may have a coordinate system 50 defined inaccordance with the borehole's long axis (the z axis) and the north side(or alternatively, the high side) of the hole (the x-axis). Theformations 18, when characterized as a plane, may have a coordinatesystem 51 defined in accordance with the normal to the plane (the z″axis) and the direction of steepest descent (the x-axis). As shown inFIG. 3, the two coordinate systems are related by two rotations.Beginning with the borehole's coordinate system (x,y,z), a firstrotation of angle γ is made about the z axis. The resulting coordinatesystem is denoted (x′,y′,z′). Angle γ is the relative strike angle,which indicates the direction of the formation dip relative to theborehole's coordinate system. A second rotation of angle α is then madeabout the y′ axis. This aligns the borehole coordinate system with theformation coordinate system. Angle α is the relative dip angle, which isthe slope angle of the beds relative to the long axis of the borehole.

The vertical resistivity is generally found to be the resistivity asmeasured perpendicular to the plane of the formation, and the horizontalresistivity is the resistivity as measured within the plane of theformation. Determination of each of these parameters (dip angle, strikeangle, vertical resistivity, and horizontal resistivity) is desirable.

FIG. 4 shows a hypothetical antenna configuration for a multi-componentelectromagnetic resistivity logging tool. (The electromagneticresistivity logging tool may be embodied as a wireline tool and as alogging while drilling tool.) A triad of transmitter coils T_(X), T_(Y)and T_(Z), each oriented along a respective axis, is provided. At leastone triad of similarly oriented receiver coils R_(1X), R_(1Y), andR_(1Z) is also provided. For receive signal measurements relative to theamplitude and phase of the transmit signal (sometimes called “absolute”measurements), only one receiver triad would be used. A second triad ofsimilarly oriented receiver coils pairs R_(2X), R_(2Y), and R_(2Z) mayalso provided when differential measurements are desired (e.g., a signalamplitude ratio or a phase difference between receiver coils orientedalong a given axis). Differential measurements may offer increasedspatial resolution.

Moran and Gianzero, in “Effects of Formation Anisotropy on ResistivityLogging Measurements” Geophysics, Vol. 44, No. 7, p. 1266 (1979), notedthat the magnetic field h in the receiver coils can be represented interms of the magnetic moments m at the transmitters and a couplingmatrix C:h=Cm  (1)In express form, equation (1) is:

$\begin{matrix}{{\begin{bmatrix}\begin{matrix}H_{x} \\H_{y}\end{matrix} \\H_{z}\end{bmatrix} = {\begin{bmatrix}C_{xx} & C_{xy} & C_{xz} \\C_{yx} & C_{yy} & C_{zz} \\C_{zx} & C_{zy} & C_{zz}\end{bmatrix}\begin{bmatrix}\begin{matrix}M_{x} \\M_{y}\end{matrix} \\M_{z}\end{bmatrix}}},} & (2)\end{matrix}$where M_(X), M_(Y), and M_(Z) are the magnetic moments (proportional totransmit signal strength) created by transmitters T_(X), T_(Y), andT_(Z), respectively. H_(X), H_(Y), H_(Z) are the magnetic fields(proportional to receive signal strength) at the receiver antennasR_(X), R_(Y), and R_(Z), respectively.

In the antenna configuration of FIG. 4, if each transmitter is fired inturn, and signal measurements are made at each receiver in response toeach firing, nine absolute or differential measurements are obtained.These nine measurements enable the determination of a complete couplingmatrix C. (C_(IJ)=a_(IJ) V_(I) ^(J), where I is the index for receiverR_(X), R_(Y), or R_(Z), J is the index for transmitter T_(X), T_(Y), orT_(Z), a_(IJ) is a constant determined by the tool design, and V_(I)^(J) is a complex value representing the signal amplitude and phaseshift measured by receiver I in response to the firing of transmitterJ.) Knowledge of the complete coupling matrix enables the determinationof dip angle, strike angle, vertical resistivity, and horizontalresistivity. A number of techniques may be used to determine theseparameters. For example, dip and strike angle may be determined fromcoupling matrix values as explained by Li Gao and Stanley Gianzero, U.S.Pat. No. 6,727,706 “Virtual Steering of Induction Tool for Determinationof Formation Dip Angle”. Given these angles, vertical and horizontalresistivity can be determined in accordance with equations provided byMichael Bittar, U.S. Pat. No. 7,019,528 “Electromagnetic WaveResistivity Tool Having a Tilted Antenna for Geosteering within aDesired Payzone”. Alternatively, a simultaneous solution for theseparameters may be found as described in the Bittar reference.

FIG. 5 shows two angles that may be used to specify the orientation of acoil antenna. The coil antenna may be considered as residing in a planehaving a normal vector. Tilt angle θ is the angle between thelongitudinal axis of the tool and the normal vector. Azimuth angle β isthe angle between the projection of the normal vector in the X-Y planeand the tool scribe line. Alternatively, in the downhole context,azimuthal angle β may represent the angle between projection of thenormal vector in the X-Y plane and the x-axis of the borehole coordinatesystem.

It is noted that three transmitter antenna orientations and threereceiver antenna orientations are employed in the antenna configurationof FIG. 4. It has been discovered that when tool rotation is exploited,it is possible to determine the fill coupling matrix with only onetransmitter and two receiver antenna orientations (or equivalently, onereceiver and two transmitter antenna orientations). Moreover, withcertain assumptions about the configuration of the formation, onetransmitter and receiver antenna orientation may be sufficient.

Before considering various tools having specific antenna configurations,the electronics common to each tool are described. FIG. 6 shows afunctional block diagram of the electronics for a resistivity tool. Theelectronics include a control module 602 that is coupled to an analogswitch 604. Analog switch 604 is configured to drive any one of thetransmitter coils T₁, T₂, T₃, T₄ with an alternating current (AC) signalfrom a signal source 606. In some embodiments, the signal sourceprovides radio frequency signals. The control module 602 preferablyselects a transmitter coil, pauses long enough for transients to dieout, then signals data storage/transmit module 610 to accept anamplitude and phase sample of the signals received by each of thereceivers. The control module 602 preferably repeats this processsequentially for each of the transmitters. The amplitude and phase shiftvalues are provided by amplitude and phase shift detector 608 which iscoupled to each of the receiver coils R₁ and R₂ for this purpose.

Control module 602 may process the amplitude and phase shiftmeasurements to obtain compensated measurements and/or measurementaverages. The raw, compensated, or averaged measurements, may betransmitted to the surface for processing to determine dip and strikeangles, vertical and horizontal resistivity, and other information suchas (i) distance to nearest bed boundary, (ii) direction of nearest bedboundary, and (iii) resistivity of any nearby adjacent beds. The datastorage/transmitter module 610 may be coupled to telemetry unit 28(FIG. 1) to transmit signal measurements to the surface. Telemetry unit28 can use any of several known techniques for transmitting informationto the surface, including but not limited to (1) mud pressure pulse; (2)hard-wire connection; (3) acoustic wave; and (4) electromagnetic waves.

FIG. 7 shows an electromagnetic resistivity logging tool 702 having onlytwo receiver antenna orientations. The tool 702 is provided with one ormore regions 706 of reduced diameter. A wire coil 704 is placed in theregion 706 and in some embodiments is spaced away from the surface ofsubassembly 702 by a constant distance. To mechanically support andprotect the coil 704, a non-conductive filler material (not shown) suchas epoxy, rubber, or ceramic may be used in the reduced diameter regions706. Coil 704 is a transmitter coil, and coils 710 and 712 are receivingcoils. In operation, transmitter coil 704 transmits an interrogatingelectromagnetic signal which propagates through the borehole andsurrounding formation. Receiver coils 710, 712 detect the interrogatingelectromagnetic signal and provide a measure of the electromagneticsignal's amplitude attenuation and phase shift. For differentialmeasurements additional receiver coils parallel to coils 710, 712 may beprovided at an axially-spaced distance. From the absolute ordifferential amplitude attenuation and phase shift measurements, thecoupling matrix components can be determined and used as the basis fordetermining formation parameters and as the basis for geosteering.

The transmitter coil 704 may be spaced approximately 30 inches from thereceiver coils 710, 712. The transmitter and receiver coils may compriseas little as one loop of wire, although more loops may provideadditional signal power. The distance between the coils and the toolsurface is preferably in the range from 1/16 inch to ¾ inch, but may belarger. Transmitter coil 704 and receiver coil 712 may each have a tiltangle of about 45° and aligned with the same azimuth angle, whilereceiver coil 710 may have a tilt angle of about 45° and an azimuth 180°apart from receiver coil 712 (or equivalently, a tilt angle of minus 45°at the same azimuth angle as receiver coil 712).

The signal measured by a tilted receiver in response to the firing of atilted transmitter can be expressed in terms of the signals V_(I) ^(Y)that would be measured by the tool of FIG. 4. When both transmitter andreceiver coils are oriented at the same azimuth angle β, the tiltedreceiver signal V_(R) is

$\begin{matrix}{V_{R} = {{\begin{bmatrix}\begin{matrix}{\sin\;\theta_{T}\cos\;\beta} \\{\sin\;\theta_{T}\sin\;\beta}\end{matrix} \\{\cos\;\theta_{T}}\end{bmatrix}^{T}\begin{bmatrix}V_{x}^{x} & V_{x}^{y} & V_{x}^{z} \\V_{y}^{x} & V_{y}^{y} & V_{y}^{z} \\V_{z}^{x} & V_{z}^{y} & V_{z}^{z}\end{bmatrix}}\begin{bmatrix}\begin{matrix}{\sin\;\theta_{R}\cos\;\beta} \\{\sin\;\theta_{R}\sin\;\beta}\end{matrix} \\{\cos\;\theta_{R}}\end{bmatrix}}} & (3)\end{matrix}$where θ_(T) is the tilt angle of the transmitter and θ_(R) is the tiltangle of the receiver. In written-out form, the tilted receiver angleis:

$\begin{matrix}{{V_{R} = \begin{bmatrix}\begin{matrix}\begin{matrix}{{V_{x}^{x}\sin\;\theta_{T}\sin\;\theta_{R}\cos^{2}\beta} + {V_{y}^{x}\sin\;\theta_{T}\sin\;\theta_{R}\sin\;\beta\;\cos\;\beta} +} \\{{V_{z}^{x}\cos\;\theta_{T}\sin\;\theta_{R}\cos\;\beta} + {V_{x}^{y}\sin\;\theta_{T}\sin\;\theta_{R}\sin\;\beta\;\cos\;\beta} +}\end{matrix} \\{{V_{y}^{y}\sin\;\theta_{T}\sin\;\theta_{R}\sin^{2}\beta} + {V_{z}^{y}\cos\;\theta_{T}\sin\;\theta_{R}\sin\;\beta} +}\end{matrix} \\{{V_{x}^{z}\sin\;\theta_{T}\cos\;\theta_{R}\cos\;\beta} + {V_{y}^{z}\sin\;\theta_{T}\cos\;\theta_{R}\sin\;\beta} +} \\{V_{z}^{{^\circ}}\cos\;\theta_{T}\cos\;\theta_{R}}\end{bmatrix}}\mspace{14mu}} & (4)\end{matrix}$

It is noted that the azimuth angle dependence for V_(y) ^(x) and V_(x)^(y) is the same (sin β cos β), the dependence for V_(z) ^(x) and V_(x)^(z) is the same (cos β), and the dependence for V_(z) ^(y) and V_(y)^(z) is the same (sin β). It may be assumed that cross couplingcomponents V_(y) ^(x) and V_(x) ^(y) are equal, but such an assumptionis not desirable for the remaining cross components (at least not indipping anisotropic beds). In that situation, the cross couplingcomponents cannot be independently determined from a single rotatingtilted transmitter-receiver pair such as transmitter coil 704 andreceiver coil 712. (Note however that the diagonal elements can still becalculated.) A second transmitter or receiver coil (e.g., receiver coil712) may be employed to provide an independent set of equations thatenable the cross-coupling values to be determined.

A linear system of equations for the measurements made by rotating tool702 is provided below. In deriving these equations, the boreholecoordinate system is chosen so that the x-axis aligns with the dipazimuth of the surrounding formation, causing V_(y) ^(x) and V_(x) ^(y)to be zero. (The dip azimuth may be found by determining the azimuthangles at which the imaginary component of the receive signal reachesits minimum magnitude. Alternatively, these components can be assumed tobe equal and can be retained in the linear system of equations.) Thesignals measured by receivers R1 (coil 712) and R2 (coil 710) at variousazimuthal angles β₁-β_(N) are:

$\begin{matrix}{{{V_{R\; 1}( \beta_{1} )} = {\frac{1}{2}\begin{bmatrix}{{V_{x}^{x}\cos^{2}\beta_{1}} + {V_{z}^{x}\cos\;\beta_{1}} + {V_{y}^{y}\sin^{2}\beta_{1}} +} \\{{V_{z}^{y}\sin\;\beta_{1}} + {V_{x}^{z}\cos\;\beta_{1}} + {V_{y}^{z}\sin\;\beta_{1}} + V_{z}^{z}}\end{bmatrix}}},} & (5.1) \\{{{V_{R\; 1}( \beta_{2} )} = {\frac{1}{2}\begin{bmatrix}{{V_{x}^{x}\cos^{2}\beta_{2}} + {V_{z}^{x}\cos\;\beta_{2}} + {V_{y}^{y}\sin^{2}\beta_{2}} +} \\{{V_{z}^{y}\sin\;\beta_{2}} + {V_{x}^{z}\cos\;\beta_{2}} + {V_{y}^{z}\sin\;\beta_{2}} + V_{z}^{z}}\end{bmatrix}}},\ldots} & (5.2) \\{{{V_{R\; 1}( \beta_{N} )} = {\frac{1}{2}\begin{bmatrix}{{V_{x}^{x}\cos^{2}\beta_{N}} + {V_{z}^{x}\cos\;\beta_{N}} + {V_{y}^{y}\sin^{2}\beta_{N}} +} \\{{V_{z}^{y}\sin\;\beta_{N}} + {V_{x}^{z}\cos\;\beta_{N}} + {V_{y}^{z}\sin\;\beta_{N}} + V_{z}^{z}}\end{bmatrix}}},} & ( {5.N} ) \\{{{V_{R\; 2}( \beta_{1} )} = {\frac{1}{2}\begin{bmatrix}{{{- V_{x}^{x}}\cos^{2}\beta_{1}} - {V_{z}^{x}\cos\;\beta_{1}} - {V_{y}^{y}\sin^{2}\beta_{1}} -} \\{{V_{z}^{y}\sin\;\beta_{1}} + {V_{x}^{z}\cos\;\beta_{1}} + {V_{y}^{z}\sin\;\beta_{1}} + V_{z}^{z}}\end{bmatrix}}},\ldots} & ( {{5.N} + 1} ) \\{{V_{R\; 2}( \beta_{N} )} = {{\frac{1}{2}\begin{bmatrix}{{{- V_{x}^{x}}\cos^{2}\beta_{N}} - {V_{z}^{x}\cos\;\beta_{N}} - {V_{y}^{y}\sin^{2}\beta_{N}} -} \\{{V_{z}^{y}\sin\;\beta_{N}} + {V_{x}^{z}\cos\;\beta_{N}} + {V_{y}^{z}\sin\;\beta_{N}} + V_{z}^{z}}\end{bmatrix}}.}} & ( {5.2\; N} )\end{matrix}$

Thus the linear system provided above has seven unknowns and 2Nequations. It is expected that the tool would perform measurements forat least 10 different azimuthal angles, and may perform measurements for16 or 32 evenly-divided azimuthal bins as shown in FIG. 13. Theorthogonal voltage components V_(I) ^(J) can be readily determined usinga linear least squares algorithm.

FIG. 8 shows an illustrative logging method which may be performed by adownhole controller, by a surface computing facility that receivesmeasurements from the tool, or performed cooperatively by both. In block802 an initial transmitter is selected. (Multi-transmitter tools arediscussed further below.) In block 804, the selected transmitter isfired, and the amplitude and phase of each receiver's response ismeasured. The tool's position and orientation are also captured and usedto associate the receiver response measurements with an azimuthal bin.(An azimuthal bin has both an angular extent and an axial extent.) Inblock 806, the current measurements are used to update the averageresponse for each receiver for the given bin.

In block 808, a test is made to determine whether additionalmeasurements are needed or will be forthcoming at the current boreholeposition. For example, in tools having multiple transmitters, it isdesired to have measurements from each transmitter. Other reasons forneeding additional measurements include having a desired number ofmeasurements within each azimuthal bin before additional processing isperformed, or having at least a given number of azimuthally differentmeasurements before additional processing is performed. If additionalmeasurements at the current position are expected, the additionalprocessing may be postponed until all the relevant measurements havebeen collected.

Once a sufficient number of measurements have been obtained at a givenposition in the borehole, the method continues with optional block 810.In block 810, compensated measurements are calculated. Compensation ismost suitable for differential receiver configurations like that shownin FIG. 14. Tool 1402 includes a pair of receivers 1410, 1412 locatedbetween equally spaced transmitters 1408, 1414. In response to thefiring of the first transmitter 1408, receivers 1410 and 1412 detectattenuation and phase shift values A₁,Φ₁ and A₂,Φ₂, from whichdifferential measurements can be determined (e.g., (Φ₂-Φ₁), or (logA₁-log A₂)). In response to the firing of the second transmitter 1414,receivers 1410 and 1412 detect attenuation and phase shift values A₄,Φ₄and A₃,Φ₃, from which differential measurements can be determined (e.g.,(Φ₄-Φ₃)). In each azimuthal bin, the differential measurement responsesto the opposing transmitters can then be averaged together to obtain acompensated measurement, i.e., a measurement in which fixed biases inthe electronics are canceled.

In block 812, the orthogonal antenna couplings are calculated based onthe compensated measurements or on the average differential or averageabsolute measurements of attenuation and phase shift in each azimuthalbin. A least squares solution to a linear system of equations (such asthat provided in equations 5.1 through 5.2N above) is calculated to findthese coupling values. In block 814, the formation parameters ofinterest are calculated based on the orthogonal antenna couplings. Thecalculation of formation parameters may employ simultaneous inversion,or alternatively, some of the formation parameters may be fixed usingoutside information, thereby simplifying the solution process for theremaining parameters.

In optional block 816, a real-time log of one or more formationparameters (e.g., horizontal resistivity and anisotropy) is updated withthe newly calculated parameter values from block 814. The log associatesthe calculated values with a depth or axial position within theborehole. Optionally, the information may also be associated withazimuthal orientations to generate a borehole image of azimuthalresistivity.

In block 818 a check is made to determine if logging information isavailable (or will become available) for additional positions within theborehole. If so, the process begins again with block 802. Otherwise, theprocess terminates.

FIGS. 7, 9-12 and 14 show various antenna configurations forillustrative electromagnetic resistivity logging tools that may besuitable alternatives for a multi-component logging tool such as thatdescribed with respect to FIG. 4. In FIG. 7, the tool includes a singletilted transmitter antenna 704 and at least one tilted receiver antenna712 that is parallel to the transmitter antenna. The use of only asingle tilted transmitter and receiver antenna orientation enables thedetermination of the diagonal coupling matrix components, and underassumptions of cross-component equality, enables the determination ofthe cross-coupling components too. However, in a preferred embodiment, asecond tilted receiver antenna 710 is provided to enable determinationof cross-coupling components while only assuming that the XY and YXcomponents are equal. Thus tools having a single transmitter and tworeceiver antenna orientations (or a single receiver and two transmitterantenna orientations) may provide the best tradeoff between complexityand completeness.

Tool 702 may have several variations. In a first variation, the roles oftransmitter and receiver are exchanged, so that transmitters coils 710and 712 are alternately fired and the response of receiver coil 704 ismeasured. As additional variations, the crossed antenna coils 710 and712 may be equally spaced in opposite directions from the antenna coil704. Antenna coils 710 and 712 may retain their role as receiversresponding to signals from transmitter coil 704, or the roles may againbe exchanged.

Tool 702 is intended for absolute measurements (i.e., attenuation andphase shift are measured relative to the transmit signal). FIG. 9 showsan illustrative tool 902 intended for compensated differentialmeasurements with different transmitter-receiver spacings. Tiltedreceiver coils 910 and 912 are parallel, and may have a tilt angle ofabout 45° and a spacing of about 8 inches. A first pair of paralleltransmitters coils 908 and 914 are equally spaced from the receiver coilmidpoint by about 32 inches, and are shown oriented parallel to thereceiver antennas. In an alternative embodiment, the paralleltransmitter coils 908 and 914 may have any tilt angle, including a tiltangle of zero (co-axial orientation). A second pair of transmitter coils904 and 916 are equally spaced from the receiver coil midpoint by about48 inches, and are parallel to the first pair of transmitter coils. Thegreater transmitter-receiver spacing enables the electromagnetic signalsto provide measurements at greater penetration depths, enabling moreaccurate formation resistivity measurements. Since all of thetransmitter coils are parallel and the receiver coils are parallel, tool902 offers only a single transmitter antenna orientation and a singlereceiver orientation, meaning that the full coupling matrix can bedetermined only with a presumption of cross-coupling equalities. In onevariation, tool 902 employs only a single receiver to absolute ratherthan differential measurements.

FIG. 10 shows an illustrative tool 1002 which also has paralleltransmitter coils and parallel receiver coils in an antenna arrangementintended for making compensated differential measurements. The parallelreceiver coils 1010 and 1012 are shown having a tilt of about 45° in anazimuth opposite to that of the transmitter coils. However, since only asingle transmitter antenna orientation and a single receiver antennaorientation are provided, tool 1002 can enable determination of the fullcoupling matrix only with a presumption of cross-coupling equalities. Inone uncompensated variation, tool 1002 omits transmitter coils 914 and916.

FIG. 11 shows an illustrative tool 1102 having parallel transmittercoils, but having receiver coils 1110 and 1112 tilted about 45° inopposite azimuthal directions. Since tool 1102 provides two receiverorientations, determination of the full coupling matrix is possible. Theconfiguration of tool 1102 enables compensated differential measurementsto be performed. In an uncompensated variation, transmitters coils 914and 916 are omitted.

FIG. 12 shows an illustrative tool 1202 having two transmitter antennaorientations and two receiver antenna orientations. Receiver antennas1210 and 1212 are co-located and tilted about 45° in opposite azimuthaldirections. A first transmitter coil pair includes transmitter coils1208 and 914 equally spaced in opposite axial directions from thereceiver antennas by about 32 inches, and a second transmitter coil pairincludes coils 1204 and 916 equally spaced in opposite axial directionsfrom the receiver antennas by about 48 inches. Each transmitter coilpair has transmitter coils tilted in opposite azimuthal directions. Theconfiguration of FIG. 12 may be employed to make compensateddifferential measurements. In a non-differential variation, one of thereceiver coils is omitted. In a second variation, the transmitter andreceiver roles are exchanged, possibly with the omission of coil 1212.The role exchange between transmitter and receiver coils may beperformed for each of the illustrative tools disclosed herein.

FIG. 14 shows an illustrative tool 1402 having a pair of parallel tiltedreceiver antennas 1410 and 1412, with a pair of parallel co-axialtransmitter antennas 1402 and 1414 equally spaced from the midpoint ofthe receiver antennas. Though this and other disclosed antennaconfigurations have only a single transmitter orientation and a singlereceiver orientation, they are nevertheless sensitive to anisotropy indipping beds and can be used to calculate the alisotropy.

As previously mentioned, components of the coupling matrix C may be usedas a basis for geosteering. With a properly oriented borehole coordinatesystem, the z-axis is indicative of the direction to the bed boundary,and the C_(XZ) and C_(ZX) components are useful for determining theboundary's proximity.

Numerous variations and modifications will become apparent to thoseskilled in the art once the above disclosure is fully appreciated. Forexample, the foregoing disclosure describes numerous antennaconfigurations in the context of a logging while drilling tool, suchantenna configurations can also be readily applied to wireline loggingtools. Furthermore, the principle of reciprocity can be applied toobtain equivalent measurements while exchanging transmitter and receiverroles for each antenna. It is intended that the following claims beinterpreted to embrace all such variations and modifications.

1. An electromagnetic resistivity logging tool that comprises: arotational position sensor; at least one transmitter antenna; a firstreceiver antenna at a first receiver antenna orientation; and a secondreceiver antenna at a second, different receiver antenna orientation;and a processor to receive at least one of a phase and amplitudemeasurement for each of the receiver antennas at each of a plurality ofazimuthal angles to calculate at least one component of a couplingmatrix using only receiver antennas having the first and second receiverantenna orientations.
 2. The tool of claim 1, wherein the processorcalculates at least seven components of the coupling matrix using onlyreceiver antennas having the first and second receiver antennaorientations.
 3. The tool of claim 2, wherein the processor furtherdetermines the seven components of the coupling matrix using onlytransmitter antennas having the same orientation as said at least onetransmitter antenna.
 4. The tool of claim 1, wherein the processoraverages measurements in bins associated with each of the plurality ofazimuthal angles and determines the coupling matrix components from theaverage measurements.
 5. The tool of claim 1, wherein the processordetermines the coupling matrix components based on a linear system ofequations that express a dependence of each receiver's response onazimuthal angle.
 6. The tool of claim 1, wherein the coupling matrixcomponents are used to determine a log of a formation parameter forstorage or display.
 7. The tool of claim 5, wherein the formationparameter is in a set consisting of anisotropy and vertical resistivity.8. The tool of claim 5, wherein the formation parameter is a formationdip angle.
 9. The tool of claim 1, wherein the processor determines ageosteering signal based at least in part on the C_(XZ) or C_(ZX)component of the coupling matrix.